Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 22 Oct 2016, 23:18

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If n and y are positive integers and 450y=n^3,

Author Message
TAGS:

### Hide Tags

Intern
Joined: 16 Oct 2012
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 8

If n and y are positive integers and 450y=n^3, [#permalink]

### Show Tags

02 Jan 2013, 20:59
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:58) correct 42% (01:27) wrong based on 57 sessions

### HideShow timer Statistics

If n and y are positive integers and 450y=n^3, which of the following must be an integer?

I. (y)/{3×(2^2)×5}

II. (y)/{(3^2)×2×5}

III. (y)/{3×2×(5^2)}

(A) None
(B) I only
(C) II only
(D) III only
(E) I, II, and III

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-and-y-are-positive-integers-and-450y-n-92562.html
[Reveal] Spoiler: OA
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 174

Kudos [?]: 1248 [1] , given: 62

Re: If n and y are positive integers and 450y=n^3, [#permalink]

### Show Tags

02 Jan 2013, 22:00
1
KUDOS
kiyo0610 wrote:
If n and y are positive integers and 450y=n^3, which of the following must be an integer?

I. (y)/{3×(2^2)×5}

II. (y)/{(3^2)×2×5}

III. (y)/{3×2×(5^2)}

(A) None
(B) I only
(C) II only
(D) III only
(E) I, II, and III

Defactorize 450.
It will come out as $$5^2 * 3^2 * 2$$.
Since n and y are integers, hence $$450y$$ will also be an integer.
To make y an integer 450 must be a factor of $$n^3$$. In order for this to happen, 5s, 3s and 2s must be in trios. When one takes the cube root, the resultant will be an integer.

Only I provides those numbers that make the 5s, 3s and 2s to become in trios. Since 450 = $$5^2 * 3^2 * 2$$, so cube root of the number that makes the resultant root an integer will be the answer.
Only I does that.
Hence B
_________________
Intern
Joined: 15 May 2012
Posts: 7
Followers: 0

Kudos [?]: 2 [0], given: 1

Re: If n and y are positive integers and 450y=n^3, [#permalink]

### Show Tags

02 Jan 2013, 23:24
n3 = 450 y
n3 = 9 x 5 x 10 y
n3 = 3 x 3 x 5 x 5 x 2 y
Because n is in its 3rd power.
This implies that
Y has to have a 3, a 5, two 2’s and may be other
(lets call it x3) as its prime factors
Thus,
Y = 3 * 5 * 2 * 2 * x3

Condn 1->y/ 3*4*5
Replacing Y with its factors
(3 * 5 * 2 * 2 * x3) / 3*4*5
Nothing left in the denominator -> Must be Integer
I is correct.

[b]Condn 2->[/b]
y/ 3*3*2*5
Replacing Y with its factors
(3 * 5 * 2 * 2 * x3) / 3*3*2*5
A 3 left in the denominator -> May be Integer
II is not correct.

Condn 3->
y/ 3*2*5*5
Replacing Y with its factors
(3 * 5 * 2 * 2 * x3) / 3*2*5*5
A 5 left in the denominator -> May be Integer III is not correct.

Ans is B
Attachments

3jan1.pdf [21.76 KiB]

Math Expert
Joined: 02 Sep 2009
Posts: 35244
Followers: 6625

Kudos [?]: 85405 [0], given: 10236

Re: If n and y are positive integers and 450y=n^3, [#permalink]

### Show Tags

03 Jan 2013, 02:36
kiyo0610 wrote:
If n and y are positive integers and 450y=n^3, which of the following must be an integer?

I. (y)/{3×(2^2)×5}

II. (y)/{(3^2)×2×5}

III. (y)/{3×2×(5^2)}

(A) None
(B) I only
(C) II only
(D) III only
(E) I, II, and III

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-and-y-are-positive-integers-and-450y-n-92562.html
_________________
Re: If n and y are positive integers and 450y=n^3,   [#permalink] 03 Jan 2013, 02:36
Similar topics Replies Last post
Similar
Topics:
7 If x and y are positive integers and 7 21 Feb 2012, 14:45
17 If (n-2)! = (n! + (n-1)!)/99, and n is a positive integer, then n=? 14 21 Nov 2010, 19:21
70 If n and y are positive integers and 450y=n^3 20 11 Apr 2010, 23:56
3 If n and y are positive integers and 450y = n^3, which of 11 09 Mar 2010, 02:50
51 If n and y are positive integers and 450y = n^3, which of 19 22 Oct 2008, 11:12
Display posts from previous: Sort by